Transcript Find an Inverse Equation Algebraically

Find an Inverse Equation
Algebraically
Find an Inverse Equation Algebraically
To find an inverse equation algebraically:
1. Switch the x and y in the equation.
2. Solve for y.
Algebraically Finding an Inverse
Find the inverse of the following:
Switch x and y
x  6 y  11
x  11  6 y
y  6 x  11
Solve for y
x 11
6
y
y
x 11
6
Do not write y-1
Make sure to check with a table and graph on the calculator.
Algebraically Finding an Inverse
Find the inverse of the following: y  2  x  7   3
2
Switch x and y
x  2  y  7  3
2
Solve for y
x  3  2  y  7
x 3
2


x 3
2
x 3
2
  y  7
 y7
2
y
2
x 3
2
7
Because x2=9 has
two solutions: 3 & -3
7  y
Make sure to check with a table and graph on the calculator.
Algebraically Finding an Inverse
Find the inverse of the following: e  x  
 x 103
4
Switch x and y
y  10 

x
Solve for y
4
4 x   y  10 
3
3
Really y =
3
3
e
1
 x 
3
4 x  10
4 x  y  10
4 x  10  y
Make sure to check with a table and graph on the calculator.
Algebraically Finding an Inverse
Only Half Parabola
Find the inverse of the following: d  x   4 x  3
Switch x and y
x  4 y 3
Really y =
Solve for y
x 3  4 y
Full Parabola
x3
 y (too much)
4
2
 x3

 y
 4 
x=3
Restrict the
Domain!
 x 3
d  x  

 4 
2
1
when x  3
Make sure to check with a table and graph on the calculator.